How Old is the Universe?

Until recently, astronomers estimated that the Big Bang occurred between 12 and 14
billion years ago. To put this in perspective, the Solar System is thought to be 4.5
billion years old and humans have existed as a genus for only a few million years.
Astronomers estimate the age of the universe in two ways: 1) by looking for the oldest
stars; and 2) by measuring the rate of expansion of the
universe and extrapolating back to the Big Bang; just as crime detectives can trace the
origin of a bullet from the holes in a wall.

Older Than the Oldest Stars?

Astronomers can place a lower limit to the age of the universe by studying globular
clusters. Globular clusters are a dense collection of roughly a million stars. Stellar
densities near the center of the globular cluster are enormous. If we lived near the
center of one, there would be several hundred thousand stars closer to us than Proxima
Centauri, the star nearest to the Sun.

The life cycle of a star depends upon its mass. High
mass stars are much brighter than low mass stars, thus they rapidly burn through their
supply of hydrogen fuel. A star like the Sun has enough fuel in its core to burn at its
current brightness for approximately 9 billion years. A star that is twice as massive as
the Sun will burn through its fuel supply in only 800 million years. A 10 solar mass star,
a star that is 10 times more massive than the Sun, burns nearly a thousand times brighter
and has only a 20 million year fuel supply. Conversely, a star that is half as massive as
the Sun burns slowly enough for its fuel to last more than 20 billion years.

All of the stars in a globular cluster formed at roughly the same time, thus they can
serve as cosmic clocks. If a globular cluster is more than 20 million years old, then all
of its hydrogen burning stars will be less massive than 10 solar masses. This implies that
no individual hydrogen burning star will be more than 1000 times brighter than the Sun. If
a globular cluster is more than 2 billion years old, then there will be no
hydrogen-burning star more massive than 2 solar masses.

The oldest globular clusters contain only stars less massive than 0.7 solar masses.
These low mass stars are much dimmer than the Sun. This observation suggests that the
oldest globular clusters are between 11 and 18 billion years old. The uncertainty in this
estimate is due to the difficulty in determining the exact distance to a globular cluster
(hence, an uncertainty in the brightness (and mass) of the stars in the cluster). Another
source of uncertainty in this estimate lies in our ignorance of some of the finer details
of stellar evolution. Presumably, the universe itself is at least as old as the oldest
globular clusters that reside in it.

Extrapolating Back to the Big Bang

An alternative approach to estimating is the age of the universe is to measure the
Hubble constant. The Hubble constant is a measure of the current expansion rate of the universe. Cosmologists use this
measurement to extrapolate back to the Big Bang. This
extrapolation depends on the history of the expansion rate which in turn depends on the
current density of the universe and on the composition of
the universe.

If the universe is flat and composed mostly of matter,
then the age of the universe is

2/(3 Ho)

where Ho is the value of the Hubble constant.

If the universe has a very low density of matter, then its extrapolated age is
larger:

1/Ho

If the universe contains a form of matter similar to the cosmological constant, then the inferred age can be even
larger.

Many astronomers are working hard to measure the Hubble constant using a variety of
different techniques. Until recently, the best estimates ranged from 65 km/sec/Megaparsec
to 80 km/sec/Megaparsec, with the best value being about 72 km/sec/Megaparsec. In more
familiar units, astronomers believe that 1/Ho is between 12 and 14 billion
years.

An Age Crisis?

If we compare the two age determinations, there is a potential crisis. If the universe
is flat, and dominated by ordinary or dark matter, the age of the universe as inferred
from the Hubble constant would be about 9 billion years. The age of the universe would be
shorter than the age of oldest stars. This contradiction implies that either 1) our
measurement of the Hubble constant is incorrect, 2) the Big Bang theory is incorrect or 3)
that we need a form of matter like a cosmological constant that implies an older age for a
given observed expansion rate.

Some astronomers believe that this crisis will pass as soon as measurements improve. If
the astronomers who have measured the smaller values of the Hubble constant are correct,
and if the smaller estimates of globular cluster ages are also correct, then all is well
for the Big Bang theory, even without a cosmological constant.

WMAP Can Measure the Age of the Universe

Measurements by the WMAP satellite can help determine the age of the universe. The detailed structure of the cosmic microwave background fluctuations depends on the
current density of the universe, the composition of the
universe and its expansion rate. As of 2013, WMAP
determined these parameters with an accuracy of
better than than 1.5%. In turn, knowing the composition with this precision, we can estimate the age of the universe to about 0.4%: 13.77 ± 0.059 billion years!

How does WMAP data enable us to determine the age of the universe is 13.77 billion years, with an uncertainty of only 0.4%? The key to this is that by knowing the composition of matter and energy density in the universe, we can use Einstein's General Relativity to compute how fast the universe has been expanding in the past. With that information, we can turn the clock back and determine when the universe had "zero" size, according to Einstein. The time between then and now is the age of the universe. There is one caveat to keep in mind that affects the certainty of the age determination: we assume that the universe is flat, which is well supported by WMAP and other data. If we relax this assumption within the allowed range, the uncertainty increase a bit. Inflation naturally predicts a very nearly flat universe.

The expansion age measured by WMAP is larger than the oldest globular clusters, so the
Big Bang theory has passed an important test using data independent of the type collected by WMAP. If the
expansion age measured by WMAP had been smaller than the oldest globular clusters, then
there would have been something fundamentally wrong about either the Big Bang theory or
the theory of stellar evolution. Either way, astronomers
would have needed to rethink many of their cherished ideas. But our current estimate of
age fits well with what we know from other kinds of measurements.